Drying kinetics driven by the shape of the air/water interface in a capillary channel

Is Unidirectional Drying in a Round Capillary Always Diffusive?

The unidirectional drying of water in cylindrical capillaries has been described since the discovery of Stefan's solution as a vapor diffusion-controlled process with a square root of time kinetics. Here we show that this well-known process actually depends on the way the capillary is closed. Experiments are performed on the evaporation of water in capillaries closed at one end with a solid material or connected to a fluid reservoir. While we recover Stefan's solution in the first case, we show that in the second situation the water plug evaporates at a constant rate with the water-air meniscus remaining pinned at the exit where evaporation proceeds. The presence of the liquid reservoir closing the capillary combined with a capillary pumping effect induces a flow of the water plug toward the evaporation front leading to a constant-rate drying, substantially faster than the prediction of Stefan's equation. Our results show that a transition from a constant-rate evaporation regime at short times to a diffusion-driven evaporation regime at long times can be observed by increasing the viscosity of the fluid in the reservoir blocking the other end of the capillary. Such transition can also be observed by connecting the capillary end to a solidifying fluid like epoxy glue.

Capillary Rising in a Tube with Corners

We studied the dynamics of a fluid rising in a capillary tube with corners. In the cornered tube, unlike the circular tube, fluid rises with two parts, the bulk part where the entire cross-section is occupied by the fluid and the finger part where the cross-section is only partially filled. Using the Onsager principle, we derive coupled time-evolution equations for the two parts. We show the following: (a) At the early stage of rising, the dynamics is dominated by the bulk part and the fluid height h₀(t) shows the same behavior as that in the circular tube. (b) At the late stage, the bulk part stops rising but the finger part continues, following the scaling law h₁(t) ∼ t^1/3. We also show that, due to the coupling between the two parts, the equilibrium bulk height is smaller than the Jurin's height, which ignores the effect of the finger part.

Monolithic Chiral Nematic Organization of Cellulose Nanocrystals under Capillary Confinement

We demonstrate bioenabled crack-free chiral nematic films prepared via a unidirectional flow of cellulose nanocrystals (CNCs) in the capillary confinement. To facilitate the uniform long-range nanocrystal organization during drying, we utilized tunicate-inspired hydrogen-bonding-rich 3,4,5-trihydroxyphenethylamine hydrochloride (TOPA) for physical cross-linking of nanocrystals with enhanced hydrogen bonding and polyethylene glycol (PEG) as a relaxer of internal stresses in the vicinity of the capillary surface. The CNC/TOPA/PEG film is organized as a left-handed chiral structure parallel to flat walls, and the inner volume of the films displayed transitional herringbone organization across the interfacial region. The resulting thin films also exhibit high mechanical performance compared to brittle films with multiple cracks commonly observed for capillary-formed pure CNC films. The chiral nematic ordering of modified TOPA-PEG-CNC material propagates through the entire thickness of robust monolithic films and across centimeter-sized surface areas, facilitating consistent, vivid iridescence, and enhanced circular polarization. The best performance that prevents the cracks was achieved for a CNC/TOPA/PEG film with a minimal, 3% amount of TOPA. Overall, we suggest that intercalation of small highly adhesive molecules to cellulose nanocrystal-polymer matrices can facilitate uniform flow of liquid crystal phase and drying inside the capillary, resulting in improvement of the ultimate tensile strength and toughness (77% and 100% increase, respectively) with controlled uniform optical reflection and enhanced circular polarization unachievable during regular drying conditions.

Particle Deposition in Drying Porous Media

The drying of porous media is a ubiquitous phenomenon in soils and building materials. The fluid often contains suspended particles. Particle deposition may modify significantly the final material, as it could be pollutants or clogging the pores, decreasing the porosity, such as in salt, in which particles and drying kinetics are coupled. Here, we used SEM and X-ray microtomography to investigate the dried porous media initially saturated by nanoparticle suspensions. As the suspensions were dried, nanoparticles formed a solid deposit, which added to the initial solid matrix and decreased the porosity. We demonstrate that since the drying occurred through the top surface, the deposit is not uniform as a function of depth. Indeed, the particles were advected by the liquid flow toward the evaporative surface; the deposit was significant over a depth that depended on the initial volume fraction, but the pore size was affected over a very narrow length. These findings were interpreted in the frame of a physical model. This study may help to design better porous media and take into account particle influence in drying processes.

Wetting equilibrium in a rectangular channel

When a capillary channel with corners is wetted by a fluid, there are regions where the fluid fills the whole cross-section and regions where only the corners are filled by the fluid. The fluid fraction of the partially-filled region, s*, is an important quantity related to the capillary pressure. We calculate the value of s* for channels with a cross-section slightly deviated from a rectangle: the height is larger in the center than those on the two short sides. We find that a small change in the cross-section geometry leads to a huge change of s*. This result is consistent with experimental observations.

Surfactant Effects on the Dynamics of Capillary Rise and Finger Formation in Square Capillaries

We investigate the influence of surfactants on capillary rise and corner flow in angular pores. We therefore study capillary rise for simple fluids and surfactant solutions, comparing square to cylindrical capillaries. We show that fingers start to form in the corners of the square capillaries when the capillary rise slows down before reaching the equilibrium height. The corner flow scales as t^1/3 and its quantitative understanding necessitates that the surface wettability is taken into account in terms of the liquid's advancing contact angle on the capillary walls inside the corner. Adding surfactants to water greatly influences the corner flow in square capillaries: depending on the nature of the surfactant, the corner flow can be either suppressed completely due to autophobic effects or enhanced due to the presence of Marangoni stresses caused by a surface tension gradient inside the liquid fingers.

Evaporation kinetics of continuous water and dispersed oil droplets

Drying of volatile oil droplets immersed in a continuous water phase was observed and analysed. Drying sample solutions were sandwiched between two glass plates and the water and oil phases were observed by confocal microscopy. In the initial stage of drying, evaporation of water was dominant and drying of the oil droplets was negligible. However, the rate of water evaporation decreased when the oil droplets were compressed. Comparison of experimental data with a diffusion model of water vapour showed that the decline in drying rates occurred earlier in the experiment than in the theoretical prediction. This implies that compression and narrowing of water paths caused the decline in the rate of water evaporation. After most water had evaporated, evaporation of the oil droplets occurred. The oil droplets did not shrink isotropically and the air-liquid interface invaded into the drying oil droplets. Cross-sectional observation by z-scanning revealed direct exposure of the oil droplets and they were pinned by the residual water phase. The water network between the oil droplets collapsed after the oil droplets had evaporated. The correlation between changes in structures and drying kinetics in both liquid phases was discussed.

Convective drying of a porous medium with a paste cover

The convective drying of a composite system made of a porous medium covered with a paste is a situation often encountered with soils, roads, building and cultural heritage materials. Here we discuss the basic mechanisms at work during the drying of a model composite system made of a homogeneous paste covering a simple granular packing. We start by reviewing the rather well-known case of the convective drying of a simple granular packing (i.e. without paste cover), which serves as a reference for physical interpretations. We show that a simple model assuming homogeneous desaturation followed by a progressive development of a dry front from the sample free surface is in agreement with observations of the internal liquid distribution variations in time. In particular, this model is able to reproduce the saturation vs. time curves of various simple granular systems, which supports our understanding of physical mechanisms at work. Then we show the detailed characteristics of drying of initially saturated model composite systems (with kaolin or cellulose paste) with the help of MRI measurements providing the liquid distribution in the sample at different times during the process up to the very last stages of drying. It appears that the granular medium is unaffected (i.e. remains saturated) during an initial period during which the paste shrinks and finally forms a sufficiently rigid porous structure which will not any more shrink later on. Then the drying process is governed by capillary effects down to very low saturation. Over a wide range of saturations both media desaturate homogeneously (within each medium) at different rates which depend on the specific porous structure of the media, so as to maintain capillary equilibrium throughout the sample. During these different stages the drying rate of the whole system remains constant. For sufficiently low saturation in the paste a dry front can develop, both in the paste and the porous medium below, and the drying rate now decreases. These results show that in a drying composite system liquid extraction can occur more or less simultaneously in the different parts of the material up to the very last stages of drying. The corresponding evolution of the distributions of liquid in the different parts of the sample also provides key information for the prediction of ion or particle transport and accumulation in the different parts of a composite system.

3D Arrays of Super-Hydrophobic Microtubes from Polypore Mushrooms as Naturally-Derived Systems for Oil Absorption

Porous materials derived from natural resources, such as Luffa sponges, pomelo peel and jute fibres, have recently emerged as oil adsorbents for water purification, due to their suitability, low environmental impact, biodegradability and low cost. Here we show, for the first time, that the porosity of the fruiting body of polypore mushrooms can be used to absorb oils and organic solvents while repelling water. We engineered the surface properties of Ganoderma applanatum fungi, of which the fruiting body consists of a regular array of long capillaries embedded in a fibrous matrix, with paraffin wax, octadecyltrichlorosilane (OTS) and trichloro(1H,1H,2H,2H-perfluorooctyl)silane. Morphological and wettability analyses of the modified fungus revealed that the OTS treatment was effective in preserving the 3D porosity of the natural material, inducing super-hydrophobicity (water contact angle higher than 150°) and improving oil sorption capacity (1.8⁻3.1 g/g). The treated fungus was also inserted into fluidic networks as a filtration element, and its ability to separate water from chloroform was demonstrated.

A note on evolution of pressure and flow within an evaporating capillary bridge

Experiments with evaporation of capillary bridges between two glass spheres show that the bridge gorge radius decreases much faster than the contact radius, distorting the original constant mean curvature bridge shape. In addition, the Laplace pressure calculated from local principal curvatures exhibits high gradients along the bridge moving external surface, most commonly with a high suction near the triple phase contact and positive pressure near the gorge. The high suction results from a negative external curvature at contact. Numerical dynamic simulations with a moving evaporating interface do not currently allow for reproducing a negative external curvature at contact. A series of static simulations are shown based on a representation of an experimentally observed interface, which does include the negative curvature at contact. The resulting Laplace pressure distribution is close to the experimental ones. Most importantly, the pressure gradients induce a consistent flow of liquid from the central area of the bridge, axially toward the solid contact, and then along the solid interface toward the contact area. The flow is believed to contribute to contact pinning. Pinning is viewed as one of the precursors of capillary bridge rupture.

Robust Chiral Organization of Cellulose Nanocrystals in Capillary Confinement

We showed large area uniformly aligned chiral photonic bioderived films from a liquid crystal phase formed by a cellulose nanocrystal (CNC) suspension placed in a thin capillary. As a result of the spatial confinement of the drying process, the interface between coexisting isotropic and chiral phases aligns perpendicular to the long axis of the capillary. This orientation facilitates a fast homogeneous growth of chiral pseudolayers parallel to the interface. Overall, the formation of organized solids takes hours vs weeks in contrast to the slow and heterogeneous process of drying from the traditional dish-cast approach. The saturation of water vapor in one end of the capillary causes anisotropic drying and promotes unidirectional propagation of the anisotropic phase in large regions that results in chiral CNC solid films with a uniformly oriented layered morphology. Corresponding ordering processes were monitored in situ at a nanoscale, mesoscale, and microscopic scale with complementary scattering and microscopic techniques. The resulting films show high orientation order at a multilength scale over large regions and preserved chiral handedness causing a narrower optical reflectance band and uniform birefringence over macroscopic regions in contrast to traditional dish-cast CNC films and those assembled in a magnetic field and on porous substrates. These thin films with a controllable and well-identified uniform morphology, structural colors, and handedness open up interesting possibilities for broad applications in bioderived photonic nanomaterials.

Effect of geometry on the dewetting of granular chains by evaporation

Understanding evaporation or drying in granular media still remains complex despite recent advancements. Evaporation depends on liquid transport across a connected film network from the bulk to the surface. In this study, we investigate the stability of film networks as a function of the geometry of granular chains of spherical grains. Using a controlled experimental approach, we vary the grain arrangement or packing and measure the height of the liquid film network during evaporation as packing shifts from loose-packed to close-packed arrangement. This height can be calculated from an equilibrium between hydrostatic pressure and the capillary pressure difference in the vertical film network. Following a simulation approach using Surface Evolver, we evaluate the pressure variation due to dewetting of the meniscus volume in the grains in both the percolating front and evaporating front within the two-phase zone of air/water mixture. Results show good agreement between model and experiment. We find that above a "critical" packing angle, the liquid continuity is broken and films connections fragment into separate, isolated capillary bridges.

Experimental investigation of water distribution in a two-phase zone during gravity-dominated evaporation

We characterize the water repartition within the partially saturated (two-phase) zone (PSZ) during evaporation from mixed wettable porous media by controlling the wettability of glass beads, their sizes, and as well the surrounding relative humidity. Here, capillary numbers are low and under these conditions, the percolating front is stabilized by gravity. Using experimental and numerical analyses, we find that the PSZ saturation decreases with the Bond number, where packing of smaller particles have higher saturation values than packing made of larger particles. Results also reveal that the extent (height) of the PSZ, as well as water saturation in the PSZ, both increase with wettability. We also numerically calculate the saturation exclusively contained in connected liquid films and results show that values are less than the expected PSZ saturation. These results strongly reflect that the two-phase zone is not solely made up of connected capillary networks but also made of disconnected water clusters or pockets. Moreover, we also find that global saturation (PSZ + full wet zone) decreases with wettability, confirming that greater quantity of water is lost via evaporation with increasing hydrophilicity. These results show that connected liquid films are favored in more-hydrophilic systems while disconnected water pockets are favored in less-hydrophilic systems.

A quantitative study of enhanced drying flux from a narrow liquid–air interface of colloidal suspensions during directional drying

Drying flux changes by the drying interfacial area of a colloidal suspension that affects the formation kinetics of particulate films.

Kinetics in directional drying of water that contains deformable non-volatile oil droplets

Herein, we report assessments of the kinetics in directional drying of water that contains non-volatile oil droplets, based on direct observations using a confocal microscope. The water was found to evaporate at a constant rate during the initial stage of drying, after which the evaporation rate decreased. The dispersed oil droplets were compressed and distorted as the surrounding water was lost. Further evaporation of water resulted in coalescence of the oil droplets, with the eventual formation of an oil layer at the drying interface. However, it was apparent that the drying rate decreased even before the formation of this oil layer. We propose that the restricted transport of water via the narrow paths between the distorted oil droplets was responsible for the decreased drying rate. A mathematical model based on foam drainage theory is proposed and describes the experimental data very well. This work also determined that the critical disjoining pressure for the oil droplets is affected by the drying rate, such that higher pressure values are associated with slow drying conditions. The drying kinetics and stability of the dispersed oil droplets are discussed.